UV Mapping behaves very weirdly
There is a mode in the UV Editor called Sync Selection.  When Sync Selection is enabled; selecting the entire model in the 3D Viewport will select everything in the UV Editor; 
however! when Sync Selection is disabled this will not happen.  

To select everything when Sync is disabled you must first select everything in the 3D Viewport and then again in the UV Editor.  This mode allows you to work on UV coords independently but will often cause the problem you are describing. 

Make sure that everything is selected in the UV Editor and then reapply the texture.
You might want to keep that little button activated all the time until you get used to it.